Determination methods of this type are used in so-called incremental position sensors. With them, the measuring signals are generally referred to as the cosine and sine signals. By evaluation of the passages through zero of the measuring signals, a coarse position is determined—to an accuracy of one signal period. By evaluating in addition the values of the cosine and sine signals themselves, it is possible to determine—within a signal period, a fine position. For ideal measuring signals x, y, this then gives the position signal φ within the signal period concerned asφ=arctan(y/x) if x>0  (1)φ=arctan(y/x)+π if x<0  (2)φ=π/2 sign(y) if x=0  (3)
In practice, however, the measuring signals x, y are not ideal, but subject to error. With the state of the art, the formulation most commonly adopted for the erroneous measuring signals x, y isx=a cos(φ+Δ)+x0  (4)y=(1+m)a sin(φ)=y0  (5)
Here, x0 and y0 are offset errors in the measuring signals x and y, m is an amplitude error and Δ is a phase error. a is a signal amplitude. Methods for determining and compensating for these error quantities are generally known.
Thus, for example, a determination method of the type mentioned in the introduction is known from DE-A-101 63 504.
Determination methods for a position signal are known, from DE-A-100 34 733, from DE-A-101 63 528 and from the technical article “Erhöhung der Genauigkeit bei Wegsystemen durch selbstlemende Kompensation systematischer Fehler” [Increasing the precision of position measuring systems by self-learning compensation of systematic errors] by B. Höscheler, conference volume on SPS[PLC]/IPC/DRIVES, Elektrische Automatisierungstechnik—Systeme und Komponenten, Fachmesse und Kongress [Electrical Automation Technology—Systems and Components, Technical Fair and Congress] 23rd-25th Nov. 1999, Nuremberg, pages 617 to 626, by which:                two sensors scan a measuring scale, which is moveable relative to the sensors and has a plurality of equally-spaced scale divisions, and thereby supply corresponding measuring signals,        for a uniform relative movement of the measuring scale the measuring signals are periodic, are essentially sinusoidal, have essentially the same amplitude, have a phase offset relative to one another which is essentially 90°, have a basic frequency which corresponds essentially with the relative movement of the measuring scale, and over the course of one period of the measuring signals the measuring scale executes a relative movement of one scale division,        by applying correction values, corrected signals are determined from the measuring signals,        using the corrected signals, a position signal of the measuring scale is determined relative to the sensors,        the correction values are adjusted,        the correction values include two offset correction values, at least one amplitude correction value and at least one phase correction value for the measuring signals.        
With the determination method according to DE-A-100 34 733 and the technical article by B. Hoscheler, the position signal is then post-corrected by means of a fine correction method, to compensate for residual errors due to harmonics in the measuring signals. However, the fine correction method described there only works satisfactorily if any changes in speed which occur are sufficiently small.
EP-A-1 046 884 discloses a method for determining a position signal with which two sensors scan a measuring scale, which is moveable relative to the sensors and has a plurality of equally-spaced scale divisions, and thereby supply corresponding measuring signals. For a uniform relative movement of the measuring scale the measuring signals are periodic, have essentially the same amplitude, are essentially sinusoidal, have a phase offset relative to one another which is essentially 90°, and have a basic frequency which corresponds essentially with the relative movement of the measuring scale. Over the course of one period of the measuring signals the measuring scale executes a relative movement of one scale division. The measuring signals are detected with a time displacement relative to one another. For one of the measuring signals, a corrected signal is determined from the measuring signals, using correction values. A position signal of the measuring scale is determined relative to the sensors by reference to the corrected signal and the other, uncorrected signal.